Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Advancing e-learning policy and practice : influences on academics’ adoption, integration and development of multimodal e-learning courses

Tertiary education is increasingly a contested space where advances in Information Communications Technologies and their application to technology-mediated e-learning environments have forced university administrators and educators to dislocate themselves from traditional correspondence modes of student engagement. Compounding this paradigmatic shift within the traditional sphere of distance education pedagogy are multiple and conflicting pressures on academics to develop flexible, engaging, cost-effective and sustainable interactive learning resources that incorporate both multimedia and hypermedia. This chapter reports on a study that examined factors that influence educators’ decision to adopt and integrate educational technology and convert traditional print-based distance education materials into interactive multimodal e-learning formats. Although the broader study was conducted in a single Australian university and investigated pedagogical, institutional and individual factors, this chapter restricts its focus to solely the pedagogical motivations and concerns of educators. It is argued that findings from the study have significance at the institutional level, particularly in terms of developing an underlying pedagogical rationale that can permeate the e-learning culture throughout the university, while at the same time, providing a roadmap for educators who are yet to fully engage with the e-learning format.

Science teacher leadership for transforming the curriculum and classroom practice

While teacher leadership is the basis for innovation and reform within schools, few international studies have focused on the leadership practices of science teachers and heads of science departments. This chapter reviews the Australasian literature that addresses the issue both directly and indirectly. The transformational practices of heads of science departments as well as influential science teachers within departments are identified in this chapter.

Bringing academics on board : encouraging institution-wide diffusion of e-learning environments

Rapid advances in educational and information communications technology (ICT)have encouraged some educators to move beyond traditional face to face and distance education correspondence modes toward a rich, technology mediated e-learning environment. Ready access to multimedia at the desktop has provided the opportunity for educators to develop flexible, engaging and interactive learning resources incorporating multimedia and hypermedia. However, despite this opportunity, the adoption and integration of educational technologies by academics across the tertiary sector has typically been slow. This paper presents the findings of a qualitative study that investigated factors influencing the manner in which academics adopt and integrate educational technology and ICT. The research was conducted at a regional Australian university, the University of Southern Queensland (USQ), and focused on the development of e-learning environments. These e-learning environments include a range of multimodal learning objects and multiple representations of content that seek to cater for different learning styles and modal preferences, increase interaction, improve learning outcomes, provide a more inclusive and equitable curriculum and more closely mirror the on campus learning experience. This focus of this paper is primarily on the barriers or inhibitors academics reported in the study, including institutional barriers, individual inhibitors and pedagogical concerns. Strategies for addressing these obstacles are presented and implications and recommendations for educational institutions are discussed.

Homework for refugee middle school students with backgrounds marked by low levels of engagement with English school literacy

Homework presents many challenges for refugees from Africa who are arriving in Australian schools with histories of little, no or severely interrupted schooling. This is evident in the emergence of school- and community-based homework help, clubs and tutoring programs for the students. The aim of this article is to describe the homework support options accessed by eight students from Burundi, Rwanda, Eritrea and Sudan who participated in a study of pedagogy for middle school-aged African refugees, and the views on homework of their parents and teachers. The article shows some tensions between family and school expectations and the dilemmas that arise for teachers in a broader context of public concern about and official policy statement on excessive and repetitive homework. It is argued that application of policy guidelines needs to account for disadvantages that potentially accrue to students who cannot design their own independent study programs. Further, it is suggested that integration of skills and meaning-based pedagogy inherent in recent approaches to literacy education has potential for ensuring that students receive the forms of homework they require.

Assessment and curriculum reform in China : the college English test and tertiary English as a foreign language education.

Educational assessment was a worldwide commonplace practice in the last century. With the theoretical underpinnings of education shifting from behaviourism and social efficiency to constructivism and cognitive theories in the past two decades, the assessment theories and practices show a widespread changing movement. The emergent assessment paradigm, with a futurist perspective, indicates a deviation away from the prevailing large scale high-stakes standardised testing and an inclination towards classroom-based formative assessment. Innovations and reforms initiated in attempts to achieve better education outcomes for a sustainable future via more developed learning and assessment theories have included the 2007 College English Reform Program (CERP) in Chinese higher education context. This paper focuses on the College English Test (CET) - the national English as a Foreign Language (EFL) testing system for non-English majors at tertiary level in China. It seeks to explore the roles that the CET played in the past two College English curriculum reforms, and the new role that testing and assessment assumed in the newly launched reform. The paper holds that the CET was operationalised to uplift the standards. However, the extended use of this standardised testing system brings constraints as well as negative washback effects on the tertiary EFL education. Therefore in the newly launched reform -CERP, a new assessment model which combines summative and formative assessment approaches is proposed. The testing and assessment, assumed a new role - to engender desirable education outcomes. The question asked is: will the mixed approach to formative and summative assessment provide the intended cure to the agony that tertiary EFL education in China has long been suffering - spending much time, yet achieving little effects? The paper reports the progresses and challenges as informed by the available research literature, yet asserts a lot needs to be explored on the potential of the assessment mix in this examination tradition deep-rooted and examination-obsessed society.

“I woke up and realised the ground had shifted”: the shifting terrain of English curriculum

The theme of this conference comes from the epitaph on the Lewis Carroll’s gravesite. “Is All our Life then But A Dream?” This seems fitting for a time when so much change in the terrain of English makes us feel as if we are somnambulating through a surrealist landscape. Like Lewis Carroll’s Alice, (Carroll, 2003) we might find ourselves at strange tea parties with bureaucratic mad hatters, and just when we think we have a grasp of applying new theory in our teaching, we fall down another rabbit hole, to swim in confusion as some queen calls out, ‘off with their heads!’. The shifting ground in English inevitably moves in response to waves of theory influencing classroom practice. Each new paradigm has claimed to liberate language learners from the flaws of the previous model. Each linguist or literary theorist who shaped the new paradigm no doubt dreamt of a new population emerging from school as more powerfully literate citizens than the previous generation.

Operationalising first year curriculum principles

This project builds on the First Year Curriculum Project that was carried out at the Queensland University of Technology (QUT) in 2006-2007 (QUT, 2007). One of the objectives of that project was “to develop principles for the Course Development processes that capture good design in first year curriculum practice” (p. 1) and this was achieved through the development of a set of broad organising principles for first year curriculum design—the First Year Curriculum Principles (FYCPs) (Kift, 2008).

Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Problem solving in a middle school robotics design classroom

Little research has been conducted on how students work when they are required to plan, build and evaluate artefacts in technology rich learning environments such as those supported by tools including flow charts, Labview programming and Lego construction. In this study, activity theory was used as an analytic tool to examine the social construction of meaning. There was a focus on the effect of teachers’ goals and the rules they enacted upon student use of the flow chart planning tool, and the tools of the programming language Labview and Lego construction. It was found that the articulation of a teacher’s goals via rules and divisions of labour helped to form distinct communities of learning and influenced the development of different problem solving strategies. The use of the planning tool flow charting was associated with continuity of approach, integration of problem solutions including appreciation of the nexus between construction and programming, and greater educational transformation. Students who flow charted defined problems in a more holistic way and demonstrated more methodical, insightful and integrated approaches to their use of tools. The findings have implications for teaching in design dominated learning environments.

Designing for engagement : building IT systems

Context The School of Information Technology at QUT has recently undertaken a major restructuring of their Bachelor of Information Technology (BIT) course. Some of the aims of this restructuring include a reduction in first year attrition and to provide an attractive degree course that meets both student and industry expectations. Emphasis has been placed on the first semester in the context of retaining students by introducing a set of four units that complement one another and provide introductory material on technology, programming and related skills, and generic skills that will aid the students throughout their undergraduate course and in their careers. This discussion relates to one of these four fist semester units, namely Building IT Systems. The aim of this unit is to create small Information Technology (IT) systems that use programming or scripting, databases as either standalone applications or web applications. In the prior history of teaching introductory computer programming at QUT, programming has been taught as a stand alone subject and integration of computer applications with other systems such as databases and networks was not undertaken until students had been given a thorough grounding in those topics as well. Feedback has indicated that students do not believe that working with a database requires programming skills. In fact, the teaching of the building blocks of computer applications have been compartmentalized and taught in isolation from each other. The teaching of introductory computer programming has been an industry requirement of IT degree courses as many jobs require at least some knowledge of the topic. Yet, computer programming is not a skill that all students have equal capabilities of learning (Bruce et al., 2004) and this is clearly shown by the volume of publications dedicated to this topic in the literature over a broad period of time (Eckerdal & Berglund, 2005; Mayer, 1981; Winslow, 1996). The teaching of this introductory material has been done pretty much the same way over the past thirty years. During this period of time that introductory computer programming courses have been taught at QUT, a number of different programming languages and programming paradigms have been used and different approaches to teaching and learning have been attempted in an effort to find the golden thread that would allow students to learn this complex topic. Unfortunately, computer programming is not a skill that can be learnt in one semester. Some basics can be learnt but it can take many years to master (Norvig, 2001). Faculty data typically has shown a bimodal distribution of results for students undertaking introductory programming courses with a high proportion of students receiving a high mark and a high proportion of students receiving a low or failing mark. This indicates that there are students who understand and excel with the introductory material while there is another group who struggle to understand the concepts and practices required to be able to translate a specification or problem statement into a computer program that achieves what is being requested. The consequence of a large group of students failing the introductory programming course has been a high level of attrition amongst first year students. This attrition level does not provide good continuity in student numbers in later years of the degree program and the current approach is not seen as sustainable.